Method and system for an alternating channel delta quantizer for MIMO pre-coders with finite rate channel state information feedback

ABSTRACT

Aspects of a method and system for an alternating channel delta quantizer for MIMO pre-coders with finite rate channel state information feedback may include quantizing a change in channel state information in a MIMO pre-coding system onto a codebook using a cost function and selecting the codebook from a set of codebooks; and generating the set of codebooks from a plurality of codebooks, where each may comprise one or more unitary matrices. The channel state information may be a matrix V that may be generated using Singular Value Decomposition (SVD) and/or Geometric Mean Decomposition (GMD). The selecting of the codebooks may be enabled by alternating between the elements of the set of codebooks. The cost function f(A) may be defined by the following relationship: 
               f   ⁡     (   A   )       =     (       1   N     ⁢       ∑     j   =   1     N     ⁢            a   jj          2         )           
where A is a matrix of size N by N and a ij  is element (i,j) of matrix A.

CROSS-REFERENCE TO RELATED APPLICATIONS/INCORPORATION BY REFERENCE

This application is a continuation of U.S. application Ser. No. 11/847,647, filed on Aug. 30, 2007, which makes reference to, claims priority to, and claims the benefit of U.S. Provisional Application Ser. No. 60/889,382, filed on Feb. 12, 2007.

This application also makes reference to:

U.S. Application Ser. No. 60/889,374, filed on Feb. 12, 2007;

U.S. Application Ser. No. 60/889,397, filed on Feb. 12, 2007;

U.S. Application Ser. No. 60/889,406, filed on Feb. 12, 2007;

U.S. application Ser. No. 11/847,628, filed on Aug. 30, 2007;

U.S. application Ser. No. 11/847,669, filed on Aug. 30, 2007; and

U.S. application Ser. No. 11/847,683, filed on Aug. 30, 2007.

Each of the above referenced applications is hereby incorporated herein by reference in its entirety for all purposes.

FIELD OF THE INVENTION

Certain embodiments of the invention relate to signal processing for communication systems. More specifically, certain embodiments of the invention relate to a method and system for an alternating channel delta quantizer for MIMO pre-coders with finite rate channel state information feedback.

BACKGROUND OF THE INVENTION

Mobile communications have changed the way people communicate and mobile phones have been transformed from a luxury item to an essential part of every day life. The use of mobile phones is today dictated by social situations, rather than hampered by location or technology. While voice connections fulfill the basic need to communicate, and mobile voice connections continue to filter even further into the fabric of every day life, the mobile Internet is the next step in the mobile communication revolution. The mobile Internet is poised to become a common source of everyday information, and easy, versatile mobile access to this data will be taken for granted.

Third generation (3G) cellular networks have been specifically designed to fulfill these future demands of the mobile Internet. As these services grow in popularity and usage, factors such as cost efficient optimization of network capacity and quality of service (QoS) will become even more essential to cellular operators than it is today. These factors may be achieved with careful network planning and operation, improvements in transmission methods, and advances in receiver techniques. To this end, carriers need technologies that will allow them to increase downlink throughput and, in turn, offer advanced QoS capabilities and speeds that rival those delivered by cable modem and/or DSL service providers.

In order to meet these demands, communication systems using multiple antennas at both the transmitter and the receiver have recently received increased attention due to their promise of providing significant capacity increase in a wireless fading environment. These multi-antenna configurations, also known as smart antenna techniques, may be utilized to mitigate the negative effects of multipath and/or signal interference on signal reception. It is anticipated that smart antenna techniques may be increasingly utilized both in connection with the deployment of base station infrastructure and mobile subscriber units in cellular systems to address the increasing capacity demands being placed on those systems. These demands arise, in part, from a shift underway from current voice-based services to next-generation wireless multimedia services that provide voice, video, and data communication.

The utilization of multiple transmit and/or receive antennas is designed to introduce a diversity gain and to raise the degrees of freedom to suppress interference generated within the signal reception process. Diversity gains improve system performance by increasing received signal-to-noise ratio and stabilizing the transmission link. On the other hand, more degrees of freedom allow multiple simultaneous transmissions by providing more robustness against signal interference, and/or by permitting greater frequency reuse for higher capacity. In communication systems that incorporate multi-antenna receivers, a set of M receive antennas may be utilized to null the effect of (M−1) interferers, for example. Accordingly, N signals may be simultaneously transmitted in the same bandwidth using N transmit antennas, with the transmitted signal then being separated into N respective signals by way of a set of N antennas deployed at the receiver. Systems that utilize multiple transmit and receive antennas may be referred to as multiple-input multiple-output (MIMO) systems. One attractive aspect of multi-antenna systems, in particular MIMO systems, is the significant increase in system capacity that may be achieved by utilizing these transmission configurations. For a fixed overall transmitted power and bandwidth, the capacity offered by a MIMO configuration may scale with the increased signal-to-noise ratio (SNR). For example, in the case of fading multipath channels, a MIMO configuration may increase system capacity by nearly M additional bits/cycle for each 3-dB increase in SNR.

The widespread deployment of multi-antenna systems in wireless communications has been limited by the increased cost that results from increased size, complexity, and power consumption. This poses problems for wireless system designs and applications. As a result, some work on multiple antenna systems may be focused on systems that support single user point-to-point links, other work may focus on multiuser scenarios. Communication systems that employ multiple antennas may greatly improve the system capacity.

To obtain significant performance gains using MIMO technology, it may however be desirable to supply information on the channel to the transmitter to allow, for example, MIMO pre-coding. MIMO pre-coding and other MIMO technologies based at the MIMO transmitter may benefit or require knowledge about the channel, referred to as channel state information (CSI). Furthermore, because many wireless systems operate in frequency division duplex (FDD) mode, the uplink and downlink connections may use different frequencies. In these instances, channel measurements may only be made available at the transmitter by measuring the channel at the receiver and feeding back the information. However, with increasing numbers of transmit and receive antennas in the MIMO system, feeding back channel state information may involve transferring large amounts of data. It may be desirable to limit feedback as much as possible without compromising performance.

Further limitations and disadvantages of conventional and traditional approaches will become apparent to one of skill in the art, through comparison of such systems with some aspects of the present invention as set forth in the remainder of the present application with reference to the drawings.

BRIEF SUMMARY OF THE INVENTION

A method and/or system for an alternating channel delta quantizer for MIMO pre-coders with finite rate channel state information feedback, substantially as shown in and/or described in connection with at least one of the figures, as set forth more completely in the claims.

These and other advantages, aspects and novel features of the present invention, as well as details of an illustrated embodiment thereof, will be more fully understood from the following description and drawings.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

FIG. 1A is a diagram illustrating exemplary cellular multipath communication between a base station and a mobile computing terminal, in connection with an embodiment of the invention.

FIG. 1B is a diagram illustrating an exemplary MIMO communication system, in accordance with an embodiment of the invention.

FIG. 2 is a block diagram illustrating an exemplary MIMO pre-coding transceiver chain model, in accordance with an embodiment of the invention.

FIG. 3 is a block diagram of an exemplary MIMO pre-coding system with finite rate channel state information feedback, in accordance with an embodiment of the invention.

FIG. 4 is a flow chart illustrating an exemplary implementation of a codebook algorithm, in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Certain embodiments of the invention may be found in a method and system for an alternating channel delta quantizer for MIMO pre-coders with finite rate channel state information feedback. Aspects of the method and system for an alternating channel delta quantizer for MIMO pre-coders with finite rate channel state information feedback may comprise quantizing a change in channel state information in a MIMO pre-coding system onto a codebook using a cost function and selecting the codebook from a set of codebooks; and generating the set of codebooks from a plurality of codebooks, where each may comprise one or more unitary matrices. The channel state information may be a matrix V that may be generated using Singular Value Decomposition (SVD) and/or Geometric Mean Decomposition (GMD). The selecting of the codebooks may be enabled by alternating between the elements of the set of codebooks. The cost function f(A) may be defined by the following relationship:

${f(A)} = \left( {\frac{1}{N}{\sum\limits_{j = 1}^{N}{a_{jj}}^{2}}} \right)$ where A is a matrix of size N by N and a_(ij) is element (i,j) of matrix A. One or more unitary matrices may be generated from at least a first set of matrices and a second set of matrices. The at least first set of matrices and the second set of matrices may be generated using Givens decomposition. By modifying a step size variable, a dynamic range of the plurality of codebooks may be modified. A resolution of the plurality of codebooks may be modified by modifying a cardinality of the plurality of codebooks. This may be achieved by modifying a set of angular levels. In the MIMO pre-coding system, an index may be transmitted of an element of the codebook, onto which the change in channel state information is quantized, from a receiver to a transmitter. The MIMO pre-coding system may comprise one or more transmit antennas and one or more receive antennas. A matrix at a transmitter of the MIMO pre-coding system may be linearly transformed with one of the unitary matrices.

FIG. 1A is a diagram illustrating exemplary cellular multipath communication between a base station and a mobile computing terminal, in connection with an embodiment of the invention. Referring to FIG. 1A, there is shown a house 120, a mobile terminal 122, a factory 124, a base station 126, a car 128, and communication paths 130, 132 and 134.

The base station 126 and the mobile terminal 122 may comprise suitable logic, circuitry and/or code that may be enabled to generate and process MIMO communication signals. Wireless communications between the base station 126 and the mobile terminal 122 may take place over a wireless channel. The wireless channel may comprise a plurality of communication paths, for example, the communication paths 130, 132 and 134. The wireless channel may change dynamically as the mobile terminal 122 and/or the car 128 moves. In some cases, the mobile terminal 122 may be in line-of-sight (LOS) of the base station 126. In other instances, there may not be a direct line-of-sight between the mobile terminal 122 and the base station 126 and the radio signals may travel as reflected communication paths between the communicating entities, as illustrated by the exemplary communication paths 130, 132 and 134. The radio signals may be reflected by man-made structures like the house 120, the factory 124 or the car 128, or by natural obstacles like hills. Such a system may be referred to as a non-line-of-sight (NLOS) communications system.

A communication system may comprise both LOS and NLOS signal components. If a LOS signal component is present, it may be much stronger than NLOS signal components. In some communication systems, the NLOS signal components may create interference and reduce the receiver performance. This may be referred to as multipath interference. The communication paths 130, 132 and 134, for example, may arrive with different delays at the mobile terminal 122. The communication paths 130, 132 and 134 may also be differently attenuated. In the downlink, for example, the received signal at the mobile terminal 122 may be the sum of differently attenuated communication paths 130, 132 and/or 134 that may not be synchronized and that may dynamically change. Such a channel may be referred to as a fading multipath channel. A fading multipath channel may introduce interference but it may also introduce diversity and degrees of freedom into the wireless channel. Communication systems with multiple antennas at the base station and/or at the mobile terminal, for example MIMO systems, may be particularly suited to exploit the characteristics of wireless channels and may extract large performance gains from a fading multipath channel that may result in significantly increased performance with respect to a communication system with a single antenna at the base station 126 and at the mobile terminal 122, in particular for NLOS communication systems.

FIG. 1B is a diagram illustrating an exemplary MIMO communication system, in accordance with an embodiment of the invention. Referring to FIG. 1B, there is shown a MIMO transmitter 102 and a MIMO receiver 104, and antennas 106, 108, 110, 112, 114 and 116. There is also shown a wireless channel comprising communication paths h₁₁, h₁₂, h₂₂, h₂₁, h_(2 NTX), h_(1 NTX), h_(NRX 1), h_(NRX 2), h_(NRX NTX), where h_(mn) may represent a channel coefficient from transmit antenna n to receiver antenna m. There may be N_(TX) transmitter antennas and N_(RX) receiver antennas. There is also shown transmit symbols x₁, x₂ and x_(NTX), and receive symbols y₁, y₂ and y_(NRX)

The MIMO transmitter 102 may comprise suitable logic, circuitry and/or code that may be enabled to generate transmit symbols x_(i) iε{1, 2, . . . N_(TX)} that may be transmitted by the transmit antennas, of which the antennas 106, 108 and 110 may be depicted in FIG. 1B. The MIMO receiver 104 may comprise suitable logic, circuitry and/or code that may be enabled to process the receive symbols y_(i) iε{1, 2, . . . N_(RX)} that may be received by the receive antennas, of which the antennas 112, 114 and 116 may be shown in FIG. 1B. An input-output relationship between the transmitted and the received signal in a MIMO system may be written as: y=Hx+n where y=[y₁, y₂, . . . y_(NRX)]^(T) may be a column vector with N_(RX) elements, .^(T) may denote a vector transpose, H=[h_(ij)]: iε{1, 2, . . . N_(RX)}; jε{1, 2, . . . N_(TX)} may be a channel matrix of dimensions N_(RX) by N_(TX), x=[x₁, x₂, . . . x_(NTX)]^(T) is a column vector with N_(TX) elements and n is a column vector of noise samples with N_(RX) elements. The channel matrix H may be written, for example, as H=UΣV^(H) using the Singular Value Decomposition (SVD), where .^(H) denotes the Hermitian transpose, U is a N_(RX) by N_(TX) unitary matrix, Σ is a N_(TX) by N_(TX) diagonal matrix and V is N_(TX) by N_(TX) unitary matrix. Other matrix decompositions that may diagonalize or transform the matrix H may be used instead of the SVD. If the receiver algorithm implemented in MIMO receiver 104 is, for example, an Ordered Successive Interference Cancellation (OSIC), other matrix decompositions that convert the matrix H to lower/upper triangular may be appropriate. One such decomposition may comprise Geometric Mean Decomposition (GMD), where H=QRP^(H), where R may be upper triangular with the geometric mean of the singular values of H on the diagonal elements, and Q and P may be unitary.

FIG. 2 is a block diagram illustrating an exemplary MIMO pre-coding transceiver chain model, in accordance with an embodiment of the invention. Referring to FIG. 2, there is shown a MIMO pre-coding system 200 comprising a MIMO transmitter 202, a MIMO baseband equivalent channel 203, a MIMO receiver 204, and an adder 208. The MIMO transmitter 202 may comprise a transmitter (TX) baseband processing block 210 and a transmit pre-coding block 214. The MIMO baseband equivalent channel 203 may comprise a wireless channel 206, a TX radio frequency (RF) processing block 212 and a receiver (RX) RF processing block 218. The MIMO receiver 204 may comprise a pre-coding decoding block 216 and a RX baseband processing block 220. There is also shown symbol vector s, pre-coded vector x, noise vector n, received vector y and channel-decoded vector y′.

The MIMO transmitter 202 may comprise a baseband processing block 210, which may comprise suitable logic, circuitry and/or code that may be enabled to generate a MIMO baseband transmit signal. The MIMO baseband transmit signal may be communicated to a transmit pre-coding block 214. A baseband signal may be suitably coded for transmission over a wireless channel 206 in the transmit pre-coding block 214 that may comprise suitable logic, circuitry and/or code that may enable it to perform these functions. The TX RF processing block 212 may comprise suitable logic, circuitry and/or code that may enable a signal communicated to the TX RF processing block 212 to be modulated to radio frequency (RF) for transmission over the wireless channel 206. The RX RF processing block 218 may comprise suitable logic, circuitry and/or code that may be enabled to perform radio frequency front-end functionality to receive the signal transmitted over the wireless channel 206. The RX RF processing block 218 may comprise suitable logic, circuitry and/or code that may enable the demodulation of its input signals to baseband. The adder 208 may depict the addition of noise to the received signal at the MIMO receiver 204. The MIMO receiver 204 may comprise the pre-coding decoding block 216 that may linearly decode a received signal and communicate it to the RX baseband processing block 220. The RX baseband processing block 220 may comprise suitable logic, circuitry and/or logic that may enable to apply further signal processing to baseband signal.

The MIMO transmitter 202 may comprise a baseband processing block 210, which may comprise suitable logic, circuitry and/or code that may be enabled to generate a MIMO baseband transmit signal. The MIMO baseband transmit signal may be communicated to a transmit pre-coding block 214 and may be the symbol vector s. The symbol vector s may be of dimension N_(TX) by 1.

The transmit pre-coding block 214 may be enabled to apply a linear transformation to the symbol vector s, so that x=Ws, where W may be of dimension N_(TX) by length of s, and x=[x₁, x₂ . . . x_(NTX)]^(T). Each element of the pre-coded vector x may be transmitted on a different antenna among N_(TX) available antennas.

The transmitted pre-coded vector x may traverse the MIMO baseband equivalent channel 203. From the N_(RX) receiver antennas, the received signal y may be the signal x transformed by the MIMO baseband equivalent channel 203 represented by a matrix H, plus a noise component given by the noise vector n. As depicted by the adder 208, the received vector y may be given by y=Hx+n=HWs+n. The received vector y may be communicated to the pre-coding decoding block 216, where a linear decoding operation B may be applied to the received vector y to obtain the decoded vector y′=B^(H)y=B^(H)HWs+B^(H)n, where B may be a complex matrix of appropriate dimensions. The decoded vector y′ may then be communicated to the RX baseband processing block 220 where further signal processing may be applied to the output of the pre-coding decoding block 216.

If the transfer function H of the MIMO baseband equivalent channel 203 that may be applied to the transmitted pre-coded vector x is known both at the MIMO transmitter 202 and the MIMO receiver 204, the channel may be diagonalized by, for example, setting W=V and B=U, where H=UΣV^(H) may be the singular value decomposition. In these instances, the channel decoded vector y′ may be given by the following relationship: y′=U ^(H) UΣV ^(H) Vs+U ^(H) n=Σs+U ^(H) n Since Σ may be a diagonal matrix, there may be no interference between the elements of symbol vector s in y′ and hence the wireless communications system may appear like a system with up to N_(TX) parallel single antenna wireless communication systems, for each element of s, up to the rank of channel matrix H which may be less or equal to N_(TX).

FIG. 3 is a block diagram of an exemplary MIMO pre-coding system with finite rate channel state information feedback, in accordance with an embodiment of the invention. Referring to FIG. 3, there is shown a MIMO pre-coding system 300 comprising a partial MIMO transmitter 302, a partial MIMO receiver 304, a Wireless channel 306, an adder 308, and a feedback channel 320. The partial MIMO transmitter 302 may comprise a transmit pre-coding block 314. The partial MIMO receiver 304 may comprise a pre-coding decoding block 316, a channel estimation block 322, a channel quantization block 310, a channel decomposition block 312, and a codebook processing block 318. There is also shown a symbol vector s, a pre-coded vector x, a noise vector n, a received vector y, and a decoded vector y′.

The transmit pre-coding block 314, the wireless channel 306, the adder 308 and the pre-coding decoding block 316 may be substantially similar to the transmit pre-coding block 214, the MIMO baseband equivalent channel 203, the adder 208 and the pre-coding decoding block 216, illustrated in FIG. 2. The channel estimation block 322 may comprise suitable logic, circuitry and/or logic to estimate the transfer function of the wireless channel 206. The channel estimate may be communicated to the channel decomposition block 312 that may be enabled by suitable logic, circuitry and/or code, to decompose the channel. In this respect, the decomposed channel may be communicated to the channel quantization block 310. The channel quantization block 310 may comprise suitable logic, circuitry and/or logic to partly quantize the channel onto a codebook. The codebook processing block 318 may comprise suitable logic, circuitry and/or logic that may be enabled to generate a codebook. The feedback channel 320 may represent a channel that may be enabled to carry channel state information from the partial MIMO receiver 304 to the partial MIMO transmitter 302.

In many wireless systems, the channel state information, that is, knowledge of the channel transfer matrix H, may not be available at the transmitter and the receiver. However, in order to utilize a pre-coding system as illustrated in FIG. 2, it may be desirable to have at least partial channel knowledge available at the transmitter. In the exemplary embodiment of the invention disclosed in FIG. 2, the MIMO transmitter 302 may require the unitary matrix V for pre-coding in the transmit pre-coding block 214 of MIMO transmitter 202.

In frequency division duplex (FDD) systems, the frequency band for communications from the base station to the mobile terminal, downlink communications, may be different from the frequency band in the reverse direction, uplink communications. Because of a difference in frequency bands, a channel measurement in the uplink may not generally be useful for the downlink and vice versa. In these instances, the measurements may only be made at the receiver and channel state information (CSI) may be communicated back to the transmitter via feedback. For this reason, the CSI may be fed back to the transmit pre-coding block 314 of the partial MIMO transmitter 302 from the partial MIMO receiver 304 via the feedback channel 320. The transmit pre-coding block 314, the wireless channel 306, and the adder 308 are substantially similar to the corresponding blocks 214, 203 and 208, illustrated in FIG. 2.

At the partial MIMO receiver 304, the received signal y may be used to estimate the channel transfer function H by Ĥ in the channel estimation block 322. The estimate may further be decomposed into, for example, a diagonal or triangular form, depending on a particular receiver implementation, as explained for FIG. 2. For example, the channel decomposition block 312 may perform an SVD: Ĥ=Û{circumflex over (Σ)}{circumflex over (V)}^(H). The matrix H and Ĥ may be rank r=N_(TX) matrices. This may be the case, for example, when the number of transmit antennas may be less or equal than the number of receive antennas, that is, N_(TX)≦N_(RX). It may be desirable to quantize the matrix {circumflex over (V)} into a matrix V_(k) of dimensions N_(TX) by N_(TX), where V_(k)=V_(k−1)·Q_(q) ⁰ may be generated from the last V_(k), that is V_(k−1), and a unitary rotation matrix Q_(q) ⁰ from a pre-defined finite set of unitary matrices C_(d)={Q_(i)}. The set of unitary matrices C_(d) may be referred to as the codebook. The matrix {circumflex over (V)} may change relatively slowly with respect to the channel update rate. In these instances, it may be more economical to send an update to the previous quantized matrix V_(k−1) instead of a new matrix V_(k) and utilize channel memory. By finding a matrix Q_(q) ⁰ from the codebook C_(d) that may generate a V_(k) that may be, in some sense, closest to the matrix {circumflex over (V)}, it may suffice to transmit the index q of the matrix Q_(q) ⁰ to the transmit pre-coding block 314. This may be achieved via the feedback channel 320 from the channel quantization block 310. The partial MIMO transmitter 302 may need to know the codebook C_(d). The codebook C_(d) may be varying much slower than the channel transfer function H and it may suffice to periodically update the codebook C_(d) in the transmit pre-coding block 314 from the codebook processing block 318 via the feedback channel 320. The codebook C_(d) may be chosen to be static or adaptive. Furthermore, the codebook C_(d) may also be chosen, adaptively or non-adaptively, from a set of codebooks, which may comprise adaptively and/or statically designed codebooks. In these instances, the partial MIMO receiver 304 may inform the partial MIMO transmitter 302 of the codebook in use at any given instant in time.

In cases where the channel matrix H may vary slowly with respect to the channel state information feedback rate, it may be possible to reduce the feedback rate further at the expense of reduced instantaneous degrees of freedom. This may be achieved, for example, by dividing a large codebook C into a plurality of K codebooks C_(k), such that

$C = {\left\{ Q_{i} \right\} = {\left\{ {{\overset{K}{\bigcup\limits_{k = 1}}C_{K}} = \left\{ Q_{i} \right\}} \right\}.}}$ The codebooks C_(k) may be chosen to comprise, for example, 1/K the elements Q_(i) of C each. In some instances, the codebooks C_(k) may be chosen non-overlapping, that is, {C_(j)={Q_(i)}∩C_(m)={Q_(j)}|j≠m}=Ø, where Ø may denote the empty set. In other instances, the codebooks C_(k) may be chosen to be overlapping, that is, {C_(j)={Q_(i)}∩C_(m)={Q_(j)}|j≠m}=˜Ø, where ˜ may denote logical ‘not’. The matrix {circumflex over (V)} may be quantized into V_(k), and one of the codebooks C_(k) may be used for quantization purposes, as the quantization codebook C_(d)ε{C_(k)|kε{1, . . . , K}}. The codebook C_(d) may alternate between the codebooks C_(k) in a round-robin fashion, for example, for different quantization instances. For example, quantization of {circumflex over (V)} into V_(k) may occur at time instants nT, where n may be an integer and T a time interval between successive quantization instances. The codebook C_(d)=C_(k) may be used whenever k=n mod K. This may require an index k at the partial MIMO receiver 304 to remain synchronized with a corresponding index at the partial MIMO transmitter 302. By dividing the codebook C in the manner described above, the quantization codebook C_(d) may comprise, for example, only 1/K elements of the codebook C at any quantization instant, that is, the cardinality of C may be, for example, |C|=2^(M)=K·|C_(d)|=K·2^(M−log) ² ^(K).

It may suffice to feedback M bits that may enable the elements within C to be indexed. By choosing the cardinality of the codebook used for quantization to be |C_(d)|=|C|/K=|C_(k)|, it may suffice to feedback M−log₂ K bits per quantization instance, as illustrated in the equation above. Since the elements of the codebook C={Q_(i)} may be rotations, using a reduced-size codebook C_(d) may be interpreted, for example, as restricting the rotations to a subset of directions at each quantization instance. Since, however, the codebook may alternate between the codebooks C_(k), a rotation around any axis (or direction) in C may be possible, but may comprise a number of successive rotations in a set of different codebooks C_(k). The feedback rate may be reduced because a reduced-size codebook C_(d) may be used for quantization. In some instances, reducing the feedback rate by restricting the cardinality of the quantization codebook C_(d) and hence the directions of available rotations may require a plurality of rotations to obtain the same result that may be achieved with fewer rotations by using a full codebook C. Hence, using alternating codebooks may be interpreted as a trade-off between the feedback data rate on the one hand, and the rate at which an arbitrary rotation may be achieved on the other hand. In many instances, however, the matrix {circumflex over (V)} may rotate slowly and it may be advantageous to trade-off speed of rotation for a reduction in feedback rate, and there may be a reduction in control information overhead on the uplink, which may result in an increase in the available data payload.

The matrix {circumflex over (V)} may be quantized into V_(k) as described by the following relationships:

Q_(q)⁰ = arg  max_(Q̂_(q) ∈ C_(d))f(V̂^(H)V_(k)) = arg  max_(Q̂_(q) ∈ C_(d))f(V̂^(H)V_(k − 1)Q̂_(q)) ${{C_{d}\left( {t = {nT}} \right)} = {\left. {C_{k} \in \left\{ C_{i} \right\}} \middle| k \right. = {n\;{mod}\; K}}};{C = {{\overset{K}{\bigcup\limits_{i = 1}}C_{i}} = \left\{ Q_{j} \right\}}}$ ${f(A)} = \left( {\frac{1}{N}{\sum\limits_{j = 1}^{N}{a_{jj}}^{2}}} \right)$ where A=[a_(ij)] and A may be of dimensions N by N. K may be the number of codebooks C_(k). C_(d) may assume the value of different sets C_(k) as a function of time, as described above. Hence, the matrix Q_(q) ⁰ may be chosen as the matrix {circumflex over (Q)}_(q) in the codebook C_(d) that may maximize the function f({circumflex over (V)}^(H)V_(k−1){circumflex over (Q)}_(q)) as defined above. The function f(.) may average the squared absolute value of the diagonal elements of its input matrix. By maximizing f(.), the matrix V_(k) may be chosen so that the product {circumflex over (V)}^(H)V_(k) may be most like an identity matrix, in some sense. The expression for f(.) above may maximize the instantaneous capacity of the pre-coded MIMO system under some approximations. Hence, the channel H may be estimated in the channel estimation block 322 and decomposed in the channel decomposition block 312.

In the channel quantization block 310, a matrix, for example {circumflex over (V)} may be quantized into a matrix V_(k)=V_(k−1)·Q_(q) ⁰ and the index q may be fed back to the partial MIMO transmitter 302 via the feedback channel 320. Less frequently than the index q, the codebook C from the codebook processing block 318 may be transmitted to the partial MIMO transmitter 302 via the feedback channel 320. The codebook C may also be chosen time invariant. Furthermore, the codebook C may also be chosen, adaptively or non-adaptively, from a set of codebooks, which may comprise adaptively and/or statically designed codebooks. To feedback the index q, L bits may suffice when the cardinality |C_(d)| of the codebook C_(d) may be less or equal to |C_(d)|≦2^(L).

The transmit pre-coding block 314 may perform, for example, the linear transformation x=V_(k)s. The pre-coding decoding block 316 at the receiver may implement the linear transformation y′=Û^(H)y.

A codebook C may comprise complex unitary matrices {Q_(q)}. A desirable codebook may be one that comprises an easily adjustable dynamic range. This may be interpreted for rotation matrices {Q_(q)} to mean that the absolute range of angles over which the set C may rotate may be adaptable or configurable, as may the granularity, that is the step size between neighboring matrices Q_(q). Adaptability of the dynamic range may allow the codebook to be adapted to a wide variety of different channel conditions. In particular, the codebook C may be adapted to the rate of change of the wireless channel matrix H.

One exemplary protocol to construct a codebook C may make use of the unitary property of the matrices {Q_(q)}. A square complex unitary matrix Q_(q) may be constructed from a plurality of diagonal matrices D_(i) and a plurality of Givens matrices G_(k,l). The matrices {Q_(q)} may be given by the following relationship:

$\begin{matrix} {Q_{q} = {\prod\limits_{i = 1}^{N_{TX} - 1}\;\left\lbrack {{D_{i}\left( {\phi_{i,i},\ldots\mspace{14mu},\phi_{{N_{TX} - 1},i}} \right)}{\prod\limits_{k = {i + 1}}^{N_{TX}}\;{G_{k,i}\left( \varphi_{k,i} \right)}}} \right\rbrack}} & (1) \end{matrix}$ where the matrices D_(i) may be of the structure given in the following relationship:

${D_{i}\left( {\phi_{i,i},\ldots\mspace{14mu},\phi_{{N_{TX} - 1},i}} \right)} = \begin{bmatrix} I_{i - 1} & 0 & 0 & \ldots & 0 \\ 0 & {\mathbb{e}}^{{j\phi}_{i,i}} & 0 & \ldots & 0 \\ 0 & 0 & \ldots & 0 & 0 \\ 0 & 0 & 0 & {\mathbb{e}}^{{j\phi}_{{N_{TX} - 1},i}} & 0 \\ 0 & 0 & 0 & 0 & 1 \end{bmatrix}$ where the angles φ_(k,l) and the index i may define the structure of D_(i). I_(k)=I_(k) may denote an identity matrix of dimensions k by k. The indices k and i and the angle φ_(k,i) may determine the matrices G_(k,i) as shown in the following relationship:

${G_{k,i}\left( \varphi_{k,i} \right)} = \begin{bmatrix} I_{k - 1} & 0 & 0 & \ldots & 0 \\ 0 & {\cos\;\varphi_{k,i}} & 0 & {\sin\;\varphi_{k,i}} & 0 \\ 0 & 0 & I_{i - k - 1} & 0 & 0 \\ 0 & {{- \sin}\;\varphi_{k,i}} & 0 & {\cos\;\varphi_{k,i}} & 0 \\ 0 & 0 & 0 & 0 & I_{N_{TX} - i} \end{bmatrix}$ The angular range in which the aforementioned angles vary may be: φ_(k,i)ε[−π/2, π/2] and φ_(k,i)ε[−π,π]. In the case where a given Q_(q) may be an identity matrix, no rotation may take place. Hence, the matrices {Q_(q)} may be close, in some sense, to an identity matrix. A codebook C may be constructed as shown in the following relationship: C={Q _(q)(φ_(k,i),φ_(k+1,i); ∀1≦i≦k≦N _(TX)−1)|φ_(k,i) =±mδ·π/2,φ_(k+1,i) =±nδ·π}m,nε{0,1,2, . . . N _(d)}  (2) where δ≦1/N_(d) may be the step size and N_(d) may be chosen a positive integer. In some instances, the variables m and n may be chosen differently. In another embodiment, m,nε{1, 2, . . . N_(d)}, for example. The step size may permit adjustment of the dynamic range of the matrices {Q_(q)}, whereby a wide range of time-varying fading channels matrices H for different rates of change may be accommodated by the above codebook construction. That is, a codebook C may be constructed from a set of matrices {Q_(q)} that may be generated from a number of angles according to equation (1). In an embodiment of the codebook, a set C may be constructed that may comprise the matrices {Q_(d)} that may be constructed from possible combinations of the set of angles φ_(k,i)=±mδ·π/2,φ_(k,i)=±nδ·π as defined in equation (2) and equation (1). From equation (1), it may be seen that the set of Q_(q) matrices may be defined by N_(TX) ²−N_(TX) angles φ_(k,i) and φ_(k,i). Due to the construction of the codebook in equation (2), each angle may take 2N_(d)+1 different values. Combining possible angle combinations in {Q_(q)} with possible values that may be assumed by the angles, may lead to a codebook with cardinality |C|=(2N_(d)+1)^((N) ^(TX) ² ^(−N) ^(TX) ⁾, that is, |C| different matrices Q_(q) may be comprised in the set C. In these instances, B=(N_(TX) ²−N_(TX))log₂(2N_(d)+1) bits may be fed back from the partial MIMO receiver 304 to the partial MIMO transmitter 302, to feed back the index q of the choice of matrix Q_(q) ⁰, in instances where, for example, C_(d)=C. If C_(d)=C_(k), and |C_(k)|=|C|/K as illustrated above, B=(N_(TX) ²−N_(TX))log₂(2N_(d)+1)−log₂(K) bits may suffice to feed back the index q of Q_(q) ⁰εC_(k), as illustrated by the following relationship: |C|=(2N _(d)+1)^((N) ^(TX) ² ^(−N) ^(TX) ⁾ =K·|C _(k) |=K·2^([(N) ^(TX) ² ^(−N) ^(TX) ^()log) ² ^((2N) ^(d) ^(+1)−log) ² ^((K)]) There may be a large number of ways to generate the codebooks C_(k) from a codebook C, where

$C = {\left\{ Q_{i} \right\} = {\left\{ {{\overset{K}{\bigcup\limits_{k = 1}}C_{K}} = \left\{ Q_{i} \right\}} \right\}.}}$ In some instances, the union of the set of codebooks C_(k) may be different from C, that is,

${\overset{K}{\bigcup\limits_{k = 1}}C_{K}} \neq {C.}$

FIG. 4 is a flow chart illustrating an exemplary implementation of a codebook algorithm, in accordance with an embodiment of the invention. An exemplary codebook generation may be started in step 402, generating a codebook as illustrated above. In step 404, variables may be initialized, for example, the step size 8, the number of angular levels N_(d), and a counter variable i=1 that may be substantially similar to the index i in equation (1). In step 406, the variable i may be compared to a threshold value determined by the number of transmit antennas N_(TX). If the variable i is less than N_(TX)−1, the process may generate a set of matrices {D_(i)}. This set {D_(i)} may be generated from matrices D_(i) that may be constructed as described above, that is, from different combination of values for the angles φ_(k,i), . . . φ_(N) _(TX) _(−1,i, φ) _(k,i)=±mδ·π/2 that may be chosen in the range φ_(k,j)ε[−π/2,π/2], as described above. In step 410, a counter variable k may be set as a function of i. The variable k may be substantially similar to the variable k in equation (1). In step 412, the variable k may be compared to a threshold determined by N_(TX). If k is less than N_(TX), the set of matrices {G_(k,i)} may be generated. This may be achieved by generating matrices G_(k,i), using different values for φ_(k,i)=±nδ·π, where the angular range may be defined as described above by φ_(k,i)ε[−π,π]. In step 416, the variable k may be incremented, and the algorithm may loop back to step 412. If the variable k exceeds N_(TX) in step 412, process step 418 may be executed. In step 418, the generated sets {D_(i)} and {G_(k,i)} may be combined to form a new set Y_(i) given by the following relationship:

$Y_{i}\left\{ {{D_{i}\left( {\phi_{i,i},\ldots\mspace{14mu},\phi_{{N_{TX} - 1},i}} \right)}{\prod\limits_{k = {i + 1}}^{N_{TX}}\;{G_{k,i}\left( \varphi_{k,i} \right)}}} \right\}$

according to equation (1). The variable i may be incremented in step 420 and the algorithm may loop back to step 406. If the variable i exceeds N_(TX)−1 in step 406, the step 422 may be executed. In step 422, the codebook C={Q_(q)} may be generated from the generated sets Y_(i), according to equation (1). This may complete the codebook generation in the end step 424.

In accordance with an embodiment of the invention, a method and system for an alternating channel delta quantizer for MIMO pre-coders with finite rate channel state information feedback may comprise quantizing a change in channel state information in a MIMO pre-coding system onto a codebook using a cost function and selecting the codebook from a set of codebooks; generating the set of codebooks from a plurality of codebooks, each of which may comprise one or more unitary matrices, as illustrated in FIG. 3. The channel state information may be a matrix V that may be generated in channel estimation block 322 using Singular Value Decomposition (SVD) and/or Geometric Mean Decomposition (GMD). The selecting of the codebooks may be enabled by alternating between the elements of the set of codebooks in codebook processing block 318, illustrated in FIG. 3. The cost function f(A) may be defined by the following relationship:

${f(A)} = \left( {\frac{1}{N}{\sum\limits_{j = 1}^{N}{a_{jj}}^{2}}} \right)$ where A is a matrix of size N by N and a_(ij) is element (i,j) of matrix A. One or more unitary matrices may be generated in the codebook processing block 318 from at least a first set of matrices and a second set of matrices. The at least first set of matrices and the second set of matrices may be generated using Givens decomposition. By modifying a step size variable, a dynamic range of the plurality of codebooks may be modified, as explained for FIG. 3 and FIG. 4. A resolution of the plurality of codebooks may be modified by modifying a cardinality of the plurality of codebooks, as explained in FIG. 3 and FIG. 4. This may be achieved by modifying a set of angular levels in the codebook processing block 318. In the MIMO pre-coding system 300, an index may be transmitted of an element of the codebook, onto which the change in channel state information is quantized, from a receiver 304 to a transmitter 302. The MIMO pre-coding system 300 may comprise one or more transmit antennas and one or more receive antennas. A matrix at a transmitter of the MIMO pre-coding system 300 may be linearly transformed at the transmit pre-coding block 314 with one of the unitary matrices.

Another embodiment of the invention may provide a machine-readable storage, having stored thereon, a computer program having at least one code section executable by a machine, thereby causing the machine to perform the steps as described above for an alternating channel delta quantizer for MIMO pre-coders with finite rate channel state information feedback.

Accordingly, the present invention may be realized in hardware, software, or a combination of hardware and software. The present invention may be realized in a centralized fashion in at least one computer system, or in a distributed fashion where different elements are spread across several interconnected computer systems. Any kind of computer system or other apparatus adapted for carrying out the methods described herein is suited. A typical combination of hardware and software may be a general-purpose computer system with a computer program that, when being loaded and executed, controls the computer system such that it carries out the methods described herein.

The present invention may also be embedded in a computer program product, which comprises all the features enabling the implementation of the methods described herein, and which when loaded in a computer system is able to carry out these methods. Computer program in the present context means any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following: a) conversion to another language, code or notation; b) reproduction in a different material form.

While the present invention has been described with reference to certain embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the present invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the present invention without departing from its scope. Therefore, it is intended that the present invention not be limited to the particular embodiment disclosed, but that the present invention will include all embodiments falling within the scope of the appended claims. 

What is claimed is:
 1. A communication circuit comprising: a memory configured to store a plurality of codebooks, each of the plurality of codebooks comprising one or more unitary rotation matrices, wherein a first codebook of the plurality of codebooks comprises a first unitary matrix that corresponds to a first rotational direction and is not in a second codebook of the plurality of codebooks, and wherein the second codebook comprises a second unitary matrix that corresponds to a second rotational direction and is not in the first codebook; and a processor configured to: quantize a change in channel state information onto a codebook of the plurality of codebooks using a cost function; and select said codebook from the plurality of codebooks as a function of time.
 2. The communication circuit according to claim 1, wherein the channel state information comprises a matrix.
 3. The communication circuit according to claim 2, wherein the channel state information matrix is generated using Singular Value Decomposition (SVD).
 4. The communication circuit according to claim 2, wherein the channel state information matrix is generated using Geometric Mean Decomposition (GMD).
 5. The communication circuit according to claim 1, wherein elements of the plurality of codebooks are rotations.
 6. The communication circuit according to claim 1, wherein the cost function is the average of the magnitude squared of the diagonal elements of a matrix.
 7. The communication circuit according to claim 1, wherein the processor is configured to generate the one or more unitary matrices from at least a first set of matrices and a second set of matrices.
 8. The communication circuit according to claim 7, wherein the first set of matrices and the second set of matrices are generated using Givens decomposition.
 9. The communication circuit according to claim 1, wherein the processor is further configured to modify a dynamic range of the plurality of codebooks by modifying a step size variable.
 10. The communication circuit according to claim 1, wherein the processor is further configured to modify a resolution of the plurality of codebooks by modifying a cardinality of the plurality of codebooks.
 11. The communication circuit according to claim 10, wherein the cardinality of the plurality of codebooks is modified by changing a set of angular levels.
 12. The communication circuit according to claim 1, wherein the processor is further configured to communicate an index of an element of the codebook from a receiver to a transmitter in a MIMO pre-coding system.
 13. The communication circuit according to claim 1, wherein the communication circuit is further configured for use in a MIMO pre-coding system comprising one or more transmit antennas and one or more receive antennas.
 14. The communication circuit according to claim 1, wherein the processor is further configured to use one of the unitary matrices to linearly transform a matrix at a transmitter of a MIMO pre-coding system.
 15. A method comprising: storing, in a memory, a plurality of codebooks, each of the plurality of codebooks comprising one or more unitary rotation matrices, wherein a first codebook of the plurality of codebooks comprises a first unitary matrix that corresponds to a first rotational direction and is not in a second codebook of the plurality of codebooks, and wherein the second codebook comprises a second unitary matrix that corresponds to a second rotational direction and is not in the first codebook; and quantizing a change in a channel state information matrix onto a codebook of the plurality of codebooks using a cost function; and selecting said codebook from the plurality of codebooks as a function of time.
 16. The method according to claim 15, wherein the cost function is the average of the magnitude squared of the diagonal elements of the channel state information matrix.
 17. The method according to claim 15, wherein elements of the plurality of codebooks are rotations.
 18. The method according to claim 15, wherein the method further comprises modifying a dynamic range of the plurality of codebooks by modifying a step size variable.
 19. The method according to claim 15, wherein the method further comprises modifying a resolution of the plurality of codebooks by modifying a cardinality of the plurality of codebooks and changing a set of angular values.
 20. A communication circuit comprising: a memory configured to store a plurality of codebooks, each of the plurality of codebooks comprising one or more unitary rotation matrices, wherein the one or more unitary rotation matrices of at least two of the plurality of codebooks partially overlap, wherein a first codebook of the plurality of codebooks comprises a first unitary matrix that corresponds to a first rotational direction and is not in a second codebook of the plurality of codebooks, and wherein the second codebook comprises a second unitary matrix that corresponds to a second rotational direction and is not in the first codebook; and a processor configured to: quantize a change in a channel state information matrix onto a codebook of the plurality of codebooks using a cost function; and select said codebook from the plurality of codebooks as a function of time. 